2.6: Linear Inequalities in Two Variables

1
2.6 Linear Inequalities in Two Variables

• A linear inequality forms a line that is shaded
  on one side.
• There are four types
• Ax By lt C Ax By gt C
• Ax By C Ax By C
• A solution to the inequality is an ordered pair
  that yields a true statement.

2
Graphing a Basic Linear Inequality

• Step 1 Graph the boundary line of the
  inequality. Use a dashed line for lt or gt a
  solid line for or .
• Step 2 To decide which side to shade, test a
  point not on the boundary line.
• If a TRUE statement happens, then shade on the
  SAME side of the line.
• If a FALSE statement happens, then shade on the
  OPPOSITE side of the line.

3
Examples

• Graph y lt -2
• Notice that the line is dashed because of the lt

4
Examples

• Graph x 1
• Notice that the line is solid because of the

5
More Sophisticated Examples

• Graph y lt 2x
• m 2 b 0
• Dashed
• Test (0, 3)
• Is 3lt2(0) ?
• FALSE

6
More Sophisticated Examples

• Graph 2x - 5y 10
• x-int 5
• y-int -2
• Test (0,0)
• 2(0) - 5(0) 10
• Is 0 10 ? FALSE!

7
Challenge Extended!

• Graph 4x 2y 8

8
Challenge Extended

• Graph y lt -3x 1